Past exam of the flows, fluctuations and complexity and symmetry and relativity paper of Part B of the physics course of the University of Oxford / 2011 / 1 / 4

Take positive circulation to mean counterclockwise in the $(x,z)$ diagram, with $x$ right and $z$ up. The upper surface is then traversed right to left. To first order in $a/b$,Thus the bound circulation is clockwise. Any exterior contour enclosing the hydrofoil has the same circulation in an irrotational flow; a globally completed two-dimensional flow must contain a circulation component decaying as $|\Gamma |/(2\pi r)$ at large distance. The simple local upper/lower velocity prescription cannot describe the entire exterior. For a start from rest, Kelvin's circulation theorem requires compensating shed vorticity, represented by a starting vortex in a physical wake.

Numerically,If the question's fluid force includes buoyancy, $B^{\prime }\simeq 1.25\times 10^3\mathrm{N}{\mathrm{m}}^{-1}$ and the total upward fluid force is about $2.05\times 10^3\mathrm{N}{\mathrm{m}}^{-1}$, using $g=9.81\mathrm{m}{\mathrm{s}}^{-2}$. Weight of the hydrofoil is not specified and is not part of this fluid force. The motion-induced lift also agrees with the Kutta–Joukowski theorem, $L^{\prime }=-\rho U_0\Gamma$ in this orientation.

The chord-based Reynolds number isAt this large Reynolds number, smooth laminar flow over the whole body is unlikely in ordinary conditions; wall layers may undergo transition and separate. A thin-layer inviscid flow approximation outside them can remain useful, but does not justify globally laminar flow.